∗
Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org
• • • v = 0, −λ∇θ · n + εgσθm4ax = −λs∇θs · n + εsσθs4, θs = θ,
Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org ∂θ ρc ∂t = −∇ · q − cg∇θ · ρgϕgv − J△e0; q = −Λ · ∇θ, ρgϕgv = −K · ∇p, J = J0e−EA/Rθ, p = ρg R θ, µ g ρ = ρfϕf + ρbϕb + ρpϕp + ρgϕg, ρc = ρfcfϕf + ρbcbϕb + ρpcpϕp + ρgcgϕg,
Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org n · ∇p = 0, n · Λ · ∇θ = 0 . º øŁ ae
2 Tαα = X(Cαβeββ + Nαβκββ) − Pgα − Tˆα,
β=1 ∂Aβ Tαα + ∂AαTαβ − ∂Aβ Tββ + ∂∂Aqβα Tαβ + Aβ AαkαQα − ∂∂Pqαg = 0, ∂Aβ∂Mqααα + ∂A∂αqMβαβ − ∂∂qAαβ Mββ + ∂∂Aqβα Mαβ − Aβ AαQα − ∂∂Pqαg = 0, ∂qα ∂qβ ∂qα
∂A2Q1 + ∂A1Q2 − (k1 + k2)A1A2ϕgPg = 0; −A1A2(k1T11 + k2T22 + pe) + ∂q1 ∂q2 α, β = 1, 2; α 6= β,
T12 = 2(C66e12 + N66κ12), 2 Mαα = X(Nαβeββ + Dαβκββ) − Mgα − Mˆα, β=1 h/2 h/2 εˆ(βj) = Z aθ1εˆ(β0)q3j dq3, εˆ(3j) = Z aθ2εˆ3q3j dq3; j = 0,1; β = 1,2; −h/2 −h/2
t εˆγ = (αfϕfBγ + αbϕbΩγ)(θ − θ0) + αpΩγ Z (θ (t) − θ (τ))ϕˆp dτ − βpϕpΩγ, γ = 1,2,3; 0 Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org
h/2 h/2 Pgα = Z pf˜α dq3; Mgα = Z pf˜αq3 dq3;
−h/2 −h/2 C¯αβ = Cα0βa(θ01), Nαβ = Cα0βa(θ11), Dαβ = Cα0βa(θ21),
C¯66 = C606a(θ01), N66 = C606a(θ11), D66 = C606a(θ21),
C¯α+3,α+3 = Cα0+3,α+3a(θ02); α = 1,2; h/2 a(θjk) = Z aθkq3j dq3; k = 1,2; j = 0,1,2 .
−h/2 ae ß º Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org 2. ˜ º ˜º Ł ª Ł Ł Ł σ33 σ33 = 6η p1 +2 p2 − Phg1 + h1 C31 a(θ01)e11 + a(θ11)κ11 − εˆ(10) + + h1 C302 a(θ01)e22 + a(θ11)κ22 − εˆ(20) − h1 C303ε(30) +
+ (p2 − p1) ξ (q3) + p1 −2 p2 + ϕgp; σ13 = 12ηh(q3) C4(04)e13a(θ02); σ23 = 12ηh(q3) C5(05)e23a(θ02); ξ (q3) = 12 − qh3 , η (q3) = 41 − qh3 2 ; Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org … ae ae ˇ … Ł, º
Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org
Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org
Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org of Couple External Gas Dynami Pro esses and Internal Heat Transfer in Hypersoni 2013. 5. P. 127 134 10. Dimitrienko, Yu.I., Zakharov, A.A., Koryakov, M.N., Syzdykov, E.K. Computer Modeling Air raft Constru tions Using Software Pa kage SIGMA // University Resear h Journal. 12. ˜Ł Ł Ł Œ .¨., Ł Ł Æ º Œ ı //´ß ŁaeºŁ º º aeae ae Ł ŒŁ 2011. Vol. 2, N. 2. P. 3 30: https://www.asdjournal.org/index.php/ASD/arti le/viewFile/11/Crowell_ASDJ2011.pdf 6. Crowell, A.R., M Namara, J.J., Miller, B.A. Hypersoni Aerothermoelasti Response ( Æ ø Ł : 14.06.2015).
Predi tion of Skin Panels Using Computational Fluid Dynami Surrogates // ASDJournal. 4. ¸ aeŁ .`., ¸ Ł º ß . 131 137. 13. ˜Ł Ł Ł Œ º Łaeº … ´.´. ˛ ŁŒ aeŒ ªŁ 3. Ł aeŒŁØ . . Ł º ßı
// International Journal of Heat Mass Transfer. 1995. Vol. 38, N 1. P. 139 146.
Intensive Heat Flows // International Journal of Engineering S ien e. 1997. Vol. 35, N. 1.
P. 15 31. 15. ˚ ºŁŒ aeŒŁØ . ., ˇ ª Łaeº ª ł Ł ªŁ Суперкомпьютерные дни в России 2015 // Russian Supercomputing Days 2015 // RussianSCDays.org Development of SIGMA software for the supercomputer simulation of coupled aerodynamic and thermomechanical processes in composite structures of high-speed aircraft Yury Dimitrienko, Mikhail Koryakov and Andrey Zakharov Keywords: coupled simulation, aerogasdynamics, thermomechanics, hypersonic flows, heatand-mass transfer, thermodecomposition, polymer composites, heat displacement, thermotension, layering, parallel processing An algorithm for the numerical simulation of coupled aerodynamic and thermomechanical processes in composite structures of high-speed aircraft is proposed, which allows to calculate all parameters of the three-dimensional aerogasdynamic flow near the surface of the aircraft, the heat exchange on the surface, the internal heat-and-mass transfer processes in the construction of thermodecomposition polymer composite material, and dynamic processes of heat displacement in the composite construction, including the effects of changes in the elastic characteristics of the composite, variable thermal deformation, shrinkage caused by thermodecomposition, the formation of the internal pore pressure in the composite. The computer-aided software package SIGMA that implements obtained algorithms and is capable to perform calculations on high-performance computers is developed. An example of the numerical solution of the coupled problem of a model composite construction of high-speed aircraft, showing the possibility of the proposed algorithm is given.